Ahorseman left the village a at a point with coordinates (2, 5) and began riding along a straight road whose direction was given by the vector v=6i+5j. then at some point he turned at a right angle; he never changed direction again until he arrived in the village b at the point with coordinates (8, 12). at the point where he made the turn he buried a jar full of silver coins. unfortunately, he forgot the coordinates of the point. can you him recover them?

The point where he  buried his treasure is (9.04,10.74)

Step-by-step explanation:

First of all, we are going to find the equation  of the line which describes the first path  crossed by the horseman.  In order to find it we have to take in account that the vector V  provides us the direction of this path. We can associate  the direction with the slope of the line. The slope is defined by the ratio of the  vertical changes to horizontal changes between two points.  

According to the V=6i+5j  we can determine that:

Vertical change (y)= 5

Horizontal change (x)=6

Slope=\frac{5}{6}

Now , using the point- slope form

The chosen point is the point where the horseman began riding (2,5). Therefore:

m=5/6

y1=5

x1=2

y-5=5/6(x-2)

y=

Since the horseman at some point turned at a right angle towards village B  and he  unchanged his direction until arrived in the village B, the second path must be described by a line perpendicular to the first path.  

We should know that two lines are perpendicular if and only if their slopes are negative reciprocals This means m1*m2=-1

m1=5/6

m2=

In order to find the equation of the second path , we will use again the point-slope form.

The chosen point is the point where is located the Village B (8,12)

The coordinates of the point where the horseman buried a jar full of silver coins  corresponds to the intersection of the path 1 and the path 2. Therefore we are going to equal the two equations of each path.

Solving this equality for x

X=8.98

Replacing this value in any of equations of the paths

y=10.74.

Finally, the point where he buried his treasure is (9.04,10.74)

sorry i need the points

step-by-step explanation:

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la parábola es el lugar

geométrico en el cual los puntos tienen una distancia idéntica, equidistantes,

de un punto denominado foco, f, y una recta denominada directriz

el radio vector de una

parábola es el segmento que existe entre un punto cualquiera y el foco.

por la ecuación se observa

que la parábola abre hacia la derecha, por lo cual podemos usar las siguientes fórmulas

la ecuación ordinaria de la

parábola es y^2 = 4px, donde p es la longitud desde el vértice de la parábola al

foco.

la fórmula de la directriz

es x + p = 0

resolviendo:

y^2-9x = 0

y^2 = 9x

4p = 9, entonces p = 9/4

entonces el foco tendrá la

coordenada f(9/4,0)

la directriz vendrá

expresada por

x + p = 0

x = -p

x = -9/4

el problema indica que la

ordenada es igual a 6, entonces

(6)^2=9x

x = 36/9

x = 4

entonces el punto al cual

hay que obtener la distancia será p(4,6)

calculando se tendrá: pf = 

pf = 6,25 u

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step-by-step explanation: